Abstract: The finite element formulation and the finite volume form ulation are compared,both formulations are conservative and the finite volume scheme is a special kind of the finite element scheme.A new finite volume scheme is proposed by modifying the time derivative term on a control volume and by using the fractional time step integration.The one dimensional purely convection flow and two dimensional convection-diffusion flow are computed by this scheme,the results are compared with the analytical solution and the finite element simulation,which shows that the present finite volume scheme has good accuracy and stability properties.